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Generalized Derivations in Prime Rings(PDF)

Transactions of Tianjin University[ISSN:1006-4982/CN:12-1248/T]

Issue:
2011年01期
Page:
75-78
Publishing date:

Info

Title:
Generalized Derivations in Prime Rings
Author(s):
WU WeiWAN Zhaoxun
School of Sciences, Tianjin University, Tianjin 300072, China
Keywords:
DOI:

Abstract:
Let R be a ring, a, b ∈ R , (D,α ) and (G, β ) be two generalized derivations of R . It is proved that if aD( x) = G( x)b for all x ∈ R , then one of the following possibilities holds: (i) If either a or b is contained in C , then α = β = 0 and there exist p, q ∈ Qr (RC ) such that D( x) = px and G( x) = qx for all x ∈ R ;(ii) If both a and b are contained in C , then either a = b = 0 or D and G are C -linearly dependent;(iii) If neither a nor b is contained in C , then there exist p, q ∈ Qr (RC ) and w ∈ Qr (R) such that α ( x) = [q, x] and β ( x) = [x, p] for all x ∈ R , whence D( x) = wx ? xq and G( x) = xp + avx with v ∈ C and aw ? pb = 0 .

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Last Update: 2011-04-07